The spatial distribution of ion flux to a sphere in a flowing collisionless plasma is calculated using a particle-in-cell code SCEPTIC. The code is validated by comparing with prior stationary-plasma and approximate calculations. Comprehensive results are provided for ion temperatures 1 and 0.1 times the electron temperature, and for Debye length from 0.01 to 100 times the probe size. A remarkable qualitatively new result is obtained: over a range of Debye lengths from roughly 0.1 to 10 times the probe radius at Ti = 0.1Te, the downstream side of the probe receives substantially higher flux density than the upstream side when the flow is subsonic. This unexpected reversal of the asymmetry reinforces the need for these fully self-consistent calculations, but renders the use of the flux ratio for Mach-probe purposes problematic, even for deriving the direction of the flow.